What is 5/16 plus 2/3? (Answer: 47/48)

Exact Answer

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Problem: What is 5/16 plus 2/3?
Formula / Expression: 5/16 + 2/3
Final Answer: 47/48
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 3 = 48.
Working: LCD(16, 3) = 48

Step 2: Convert to Equivalent Fractions with Common Denominator 48
Multiply the numerator and denominator of 5/16 by 3, and multiply the numerator and denominator of 2/3 by 16 so both fractions share the common base 48.
Working: 5 × 3/16 × 3 = 15/48 and 2 × 16/3 × 16 = 32/48

Step 3: Add the Numerators
Now add the numerators (15 + 32 = 47) and keep the common denominator 48 unchanged.
Working: 15 + 32/48 = 47/48

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 48 is 1, confirming that 47/48 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 48 produces a repeating decimal (approximately 0.979167, or 97.9167%).
Working: 47 ÷ 48 = 0.979167 (97.9167%)

Key Values:
- Simplified Fraction: 47/48
- Mixed Number Form: 47/48
- Decimal Value: 0.979167
- Percentage: 97.9167%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-16-plus-2-3/
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5/16 + 2/3 = 47/48

Simplified Fraction

47/48

Mixed Number

Proper (47/48)

Decimal Value

0.979167

Percentage

97.9167%

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Step-by-Step Solution: 5/16 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 3 = 48.

LCD(16, 3) = 48

Step 2

Convert to Equivalent Fractions with Common Denominator 48

Multiply the numerator and denominator of 5/16 by 3, and multiply the numerator and denominator of 2/3 by 16 so both fractions share the common base 48.

5 × 3/16 × 3 = 15/48 and 2 × 16/3 × 16 = 32/48

Step 3

Add the Numerators

Now add the numerators (15 + 32 = 47) and keep the common denominator 48 unchanged.

15 + 32/48 = 47/48

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 48 is 1, confirming that 47/48 cannot be reduced further—it is already in its simplest irreducible form.

47/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 48 produces a repeating decimal (approximately 0.979167, or 97.9167%).

47 ÷ 48 = 0.979167 (97.9167%)

Visual Representation

The diagram below illustrates 5/16 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/48`
Mixed Number Form	`47/48`
Decimal Form	`0.979167`
Percentage	`97.9167%`

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Frequently Asked Questions

What is 5/16 plus 2/3 as a fraction?

5/16 + 2/3 in simplest fraction form is 47/48.

What is 5/16 plus 2/3 as a decimal?

5/16 + 2/3 converted to a decimal is 0.979167.

What is 5/16 plus 2/3 as a percentage?

5/16 + 2/3 expressed as a percentage is 97.9167%.

Does 5/16 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.979167...) because the denominator contains prime factors other than 2 and 5.